Ultraspherical Function

A function defined by a Power Series whose coefficients satisfy the Recurrence Relation

$$a_{j+2} = a_j {(k+j)(k+j+2\alpha)-n(n+2\alpha)\over (k+j+1)(k+j+2)}.$$

For $x \not = -1$, the function converges for $\alpha < 1/2$ and diverges for $\alpha>1/2$.